Players would scuff the snowy and icy turf with their feet to set up field goal attempts, because, as Patriots quarterback Drew Bledsoe said, “We couldn’t find a convict to run the snow plow,” referring to the game vs. Miami in 1982, when the late Mark Henderson, a convict, came onto the field in his tractor to clear a spot for John Smith to kick the winning field goal.

But the Patriots conquered the elements and Doug Flutie and the Buffalo Bills, 13-10, on Adam Vinatieri’s 24-yard field goal with 19 seconds remaining in overtime. On a day not fit for humans to be outdoors, the announced crowd was 42,230.

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“I’m very proud of the guys in that locker room,” he said. “I’m disappointed we didn’t play this way more often. We would have won a few more games. Hopefully we learn from this.”

The 5-10 Patriots fumbled five times and recovered all of them. Their miscues on a horrible day didn’t cost them as badly as the Bills’ two turnovers in the red zone early in the game.

The Patriots’ Lee Johnson, who set the record for career punts in the NFL (1,155), fumbled twice, once on a punt, which was recovered by Rod Rutledge for a 25-yard loss, and once on a critical hold on what would have been a winning 27-yard field goal by Vinatieri with one second left in regulation.

Still, Johnson punted wonderfully in the tough conditions, with a 42.3-yard average on seven kicks, four of them inside the 20-yard line.

It all came down to OT, however. It’s no coincidence that these teams have battled to a 42-39-1 record (advantage New England) since 1960, and that their last three meetings have gone to OT.

The Bills won the toss and elected to kick and take the wind. Belichick said he would have done the same thing.

Matthew J. Lee/Globe Staff

Vinatieri embraced Bills QB Doug Flutie after the game.

The Patriots, who ran the ball 48 times for 189 yards (3.9 yards per carry), couldn’t move on their first drive of the extra session. The Bills made four first downs on their first OT drive going from their 28 to the Patriot 12. But when Steve Christie attempted the 30-yard field goal that would have won it, Chad Eaton, who made 12 tackles, had two sacks, and blocked two kicks, got his right forearm up and blocked it.

“It got cold,” said Eaton. “I was real proud of how we hung in there as a team, and the least I could do was make a play.”

The Patriots took over at the 11, with the snow making it difficult to see, and the turf so slick it was difficult to stay up.

Bledsoe, who was 13 for 26 for 156 yards, made a couple of 17-yard throws to tight end Jermaine Wiggins, and a key backward pass to Troy Brown that he lugged 20 yards. On fourth and 5 from the Bills’ 30, the Patriots caught a break when cornerback Chris Watson pushed Terry Glenn (six catches, 70 yards) and the official called defensive interference to give the Patriots a first down at the 21.

Faced with a third-and-6 at the Bills’ 17 on a day in which no field goal attempt was automatic, Bledsoe scooted 14 yards to the right side to the 3.

A delay of game set the Patriots back 5 yards. Finally, on third down, with 23 seconds remaining, Belichick called for the field goal team.

This time Johnson made the hold. Vinatieri made the kick.

“I felt if I hit it hard, it was gonna go through,” said Vinatieri. “Once Lee got the ball down I shortened my steps and followed through the best I could.”

Bledsoe said the team changed a lot of its plays before the game and added some new ones.

If the Patriots had been able to run all season the way they did yesterday, their record might have been flip-flopped. J.R. Redmond ran for 66 yards on 20 carries until he sprained an ankle in the third quarter. Kevin Faulk came in and gained 52 yards on 14 carries, including a 13-yard touchdown with 4:45 remaining in regulation.

It was 3-3 at halftime, and scoreless in the third quarter. The Bills were about to score moments into the fourth, but Antowain Smith fumbled a handoff from Flutie at the Patriots’ 1 and it was recovered by Garrett Johnson.

But the Bills went on to take a 10-3 lead on a four-play drive when Flutie threw to tight end Jay Riemersma for 19 yards, then scooted 32 yards on a rollout to the Patriot 1. Flutie threw to backup tight end Sheldon Jackson for the score with 11:31 remaining.

Later in the quarter, a 27-yard punt by Chris Mohr set up the Patriots at the Bills’ 37. Three running plays and a pass set the stage for Faulk’s nifty scamper off right tackle, tying the score at 10 with 4:45 left.

The Patriots’ defense, called out by the coach earlier in the week for its inability to handle complicated schemes, responded by stuffing Flutie. Eaton and Willie McGinest had sacks on Flutie, pushing the Bills back to their 46 and setting up a fourth-and-29.

The Patriots got the ball back with 31 seconds left. A pair of 19-yard passes to Glenn and a 21-yard pass to Tony Carter got them to the Bills’ 10. But on the field goal try, the snap from Lonie Paxton went between Johnson’s hands, and though Vinatieri tried to one-step it as Johnson finally got it down, the kick went nowhere.

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